Ecrit par ✅ Quiz : Oscillateur Harmonique
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
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{
"quiz_title": "Oscillateur Harmonique",
"quiz_slug": "08_oscillateur_harmonique_quiz",
"quiz_description": "Quiz Edu509 : Oscillateur Harmonique",
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"time_value": 0,
"time_type": "minutes"
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"questions": [
{
"question_order": 1,
"question_title": "Quelle est l’expression correcte de la force de rappel exercée par un ressort sur un bloc dans un oscillateur harmonique ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La force de rappel d’un ressort est donnée par la loi de Hooke : \\\\( F = -k x \\\\), où \\\\( k \\\\) est la constante de raideur et \\\\( x \\\\) le déplacement par rapport à l’équilibre.",
"answers": [
{
"answer_title": "\\\\( F = -k x \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( F = k x \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( F = m x \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( F = -m x \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un bloc de \\\\( 0{,}5 \\\\mathrm{kg} \\\\) est attaché à un ressort de constante \\\\( 2{,}0 \\\\mathrm{N/m} \\\\). Quelle est la période d’oscillation du système ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période est \\\\( T = 2\\\\pi \\\\sqrt{\\\\frac{m}{k}} = 2\\\\pi \\\\sqrt{\\\\frac{0{,}5}{2{,}0}} = \\\\pi \\\\approx 3{,}14 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( 3{,}14 \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}00 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 2{,}00 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}50 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Quelle est la formule de la pulsation propre \\\\( \\\\omega \\\\) d’un oscillateur harmonique de masse \\\\( m \\\\) et de constante de raideur \\\\( k \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation propre est définie par \\\\( \\\\omega = \\\\sqrt{\\\\frac{k}{m}} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\omega = \\\\sqrt{\\\\frac{k}{m}} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\omega = \\\\sqrt{\\\\frac{m}{k}} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\omega = \\\\frac{k}{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\omega = \\\\frac{m}{k} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Un oscillateur harmonique a une amplitude de \\\\( 0{,}10 \\\\mathrm{m} \\\\) et une pulsation \\\\( \\\\omega = 2{,}0 \\\\mathrm{rad/s} \\\\). Quelle est sa vitesse maximale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La vitesse maximale est \\\\( v_{\\\\text{max}} = \\\\omega A = 2{,}0 \\\\times 0{,}10 = 0{,}20 \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}20 \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}10 \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}05 \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}00 \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Pour un oscillateur harmonique, quelle(s) grandeur(s) reste(nt) constante(s) en l’absence de frottement ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "En l’absence de frottement, l’énergie mécanique totale et la période restent constantes. L’énergie cinétique et potentielle varient au cours du mouvement.",
"answers": [
{
"answer_title": "L’énergie mécanique totale",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "L’énergie cinétique",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "L’énergie potentielle",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La période",
"is_correct": true,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Un bloc de \\\\( 0{,}2 \\\\mathrm{kg} \\\\) oscille avec une amplitude de \\\\( 5{,}0 \\\\mathrm{cm} \\\\) sur un ressort de constante \\\\( 1{,}8 \\\\mathrm{N/m} \\\\). Quelle est l’énergie mécanique totale du système ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie mécanique totale est \\\\( E = \\\\frac{1}{2}kA^2 = 0{,}5 \\\\times 1{,}8 \\\\times (0{,}050)^2 = 0{,}00225 \\\\mathrm{J} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}00225 \\\\mathrm{J} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}0180 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}00045 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}225 \\\\mathrm{J} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Quelle est l’équation différentielle du mouvement pour un oscillateur harmonique de masse \\\\( m \\\\) et de constante \\\\( k \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’équation différentielle correcte est \\\\( m \\\\frac{d^2x}{dt^2} + kx = 0 \\\\).",
"answers": [
{
"answer_title": "\\\\( m \\\\frac{d^2x}{dt^2} + kx = 0 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( m \\\\frac{dx}{dt} + kx = 0 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( m \\\\frac{d^2x}{dt^2} - kx = 0 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( m \\\\frac{dx}{dt} - kx = 0 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Un pendule simple de longueur \\\\( 1{,}0 \\\\mathrm{m} \\\\) oscille près de l’équilibre. Quelle est sa période d’oscillation ? (\\\\( g = 9{,}8 \\\\mathrm{m/s^2} \\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période est \\\\( T = 2\\\\pi \\\\sqrt{\\\\frac{l}{g}} = 2\\\\pi \\\\sqrt{\\\\frac{1{,}0}{9{,}8}} = 2{,}00 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( 2{,}00 \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}00 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 3{,}14 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}98 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Quelle(s) grandeur(s) détermine(nt) la période d’un oscillateur harmonique masse-ressort ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période dépend de la masse et de la constante du ressort : \\\\( T = 2\\\\pi \\\\sqrt{\\\\frac{m}{k}} \\\\). Elle ne dépend ni de l’amplitude ni de la phase initiale.",
"answers": [
{
"answer_title": "La masse du bloc",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La constante de raideur du ressort",
"is_correct": true,
"answer_order": 2
},
{
"answer_title": "L’amplitude",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La phase initiale",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Un oscillateur harmonique a pour équation \\\\( x(t) = 0{,}060 \\\\cos(2{,}24 t) \\\\). Quelle est son amplitude ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’amplitude est le coefficient devant le cosinus : \\\\( 0{,}060 \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}060 \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}24 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}224 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}0060 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Pour un oscillateur harmonique, à quel(s) instant(s) l’énergie cinétique est-elle maximale ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie cinétique est maximale à la position d’équilibre, où la vitesse est maximale et l’énergie potentielle minimale.",
"answers": [
{
"answer_title": "Lorsque le bloc passe par la position d’équilibre",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Lorsque le bloc est à l’amplitude maximale",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Lorsque la vitesse est nulle",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Lorsque l’énergie potentielle est minimale",
"is_correct": true,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Un bloc de \\\\( 0{,}3 \\\\mathrm{kg} \\\\) est fixé à un ressort de constante \\\\( 1{,}5 \\\\mathrm{N/m} \\\\). Quelle est la pulsation \\\\( \\\\omega \\\\) du système ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation est \\\\( \\\\omega = \\\\sqrt{\\\\frac{k}{m}} = \\\\sqrt{\\\\frac{1{,}5}{0{,}3}} = \\\\sqrt{5} = 2{,}24 \\\\mathrm{rad/s} \\\\).",
"answers": [
{
"answer_title": "\\\\( 2{,}24 \\\\mathrm{rad/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}50 \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}30 \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 3{,}00 \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Quelle est l’expression correcte de l’énergie mécanique totale d’un oscillateur harmonique ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’énergie mécanique totale est la somme de l’énergie cinétique et de l’énergie potentielle élastique : \\\\( E = \\\\frac{1}{2} m v^2 + \\\\frac{1}{2} k x^2 \\\\).",
"answers": [
{
"answer_title": "\\\\( E = \\\\frac{1}{2} m v^2 + \\\\frac{1}{2} k x^2 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( E = m v^2 + k x^2 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( E = \\\\frac{1}{2} m v^2 - \\\\frac{1}{2} k x^2 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( E = m v^2 - k x^2 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Un oscillateur harmonique a une période de \\\\( 2{,}80 \\\\mathrm{s} \\\\). Quelle est sa fréquence ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La fréquence est \\\\( f = \\\\frac{1}{T} = \\\\frac{1}{2{,}80} = 0{,}357 \\\\mathrm{Hz} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}357 \\\\mathrm{Hz} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 2{,}80 \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}280 \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 3{,}57 \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Pour un oscillateur harmonique, que représente la phase initiale \\\\( \\\\varphi_0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La phase initiale \\\\( \\\\varphi_0 \\\\) indique la position de départ de l’oscillation à l’instant \\\\( t = 0 \\\\).",
"answers": [
{
"answer_title": "La position de départ de l’oscillation à \\\\( t = 0 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La vitesse maximale",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "L’amplitude",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La période",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Un bloc de \\\\( 0{,}4 \\\\mathrm{kg} \\\\) fixé à un ressort de \\\\( 3{,}2 \\\\mathrm{N/m} \\\\) est écarté de \\\\( 8{,}0 \\\\mathrm{cm} \\\\) et reçoit une vitesse initiale de \\\\( 0{,}6 \\\\mathrm{m/s} \\\\) vers l’équilibre. Quelle est l’amplitude de l’oscillation ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’amplitude est \\\\( A = \\\\sqrt{x_0^2 + \\\\left(\\\\frac{v_0}{\\\\omega}\\\\right)^2} = 0{,}226 \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "\\\\( 0{,}226 \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}080 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}400 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}060 \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Dans l’équation \\\\( x(t) = A \\\\cos(\\\\omega t + \\\\varphi_0) \\\\), que représente \\\\( \\\\omega \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans cette équation, \\\\( \\\\omega \\\\) est la pulsation, exprimée en radians par seconde.",
"answers": [
{
"answer_title": "La pulsation (en rad/s)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "L’amplitude",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La période",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La phase initiale",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Un oscillateur harmonique a une énergie mécanique totale de \\\\( 0{,}0027 \\\\mathrm{J} \\\\) et une amplitude de \\\\( 0{,}060 \\\\mathrm{m} \\\\). Quelle est la constante de raideur du ressort ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On utilise \\\\( E = \\\\frac{1}{2}kA^2 \\\\Rightarrow k = \\\\frac{2E}{A^2} = \\\\frac{2 \\\\times 0{,}0027}{(0{,}060)^2} = 1{,}5 \\\\mathrm{N/m} \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}5 \\\\mathrm{N/m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0{,}27 \\\\mathrm{N/m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 2{,}7 \\\\mathrm{N/m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 0{,}15 \\\\mathrm{N/m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Pour un oscillateur harmonique, que se passe-t-il si on double la masse du bloc, toutes choses égales par ailleurs ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période est \\\\( T = 2\\\\pi \\\\sqrt{\\\\frac{m}{k}} \\\\). Si la masse double, la période augmente.",
"answers": [
{
"answer_title": "La période augmente",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La période diminue",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La période ne change pas",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La fréquence augmente",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un oscillateur harmonique a une équation \\\\( x(t) = 0{,}050 \\\\cos(3 t + 0{,}5) \\\\). Quelle est sa phase initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La phase initiale est le terme ajouté à \\\\( 3t \\\\) dans le cosinus, soit \\\\( 0{,}5 \\\\) radian.",
"answers": [
{
"answer_title": "\\\\( 0{,}5 \\\\) rad",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 3 \\\\) rad",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 0{,}050 \\\\) rad",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}0 \\\\) rad",
"is_correct": false,
"answer_order": 4
}
]
}
]
}